Best Known (23, 49, s)-Nets in Base 49
(23, 49, 344)-Net over F49 — Constructive and digital
Digital (23, 49, 344)-net over F49, using
- t-expansion [i] based on digital (21, 49, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(23, 49, 480)-Net over F49 — Digital
Digital (23, 49, 480)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4949, 480, F49, 26) (dual of [480, 431, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4949, 481, F49, 26) (dual of [481, 432, 27]-code), using
- an extension Ce(25) of the narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(4949, 481, F49, 26) (dual of [481, 432, 27]-code), using
(23, 49, 277264)-Net in Base 49 — Upper bound on s
There is no (23, 49, 277265)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 66011 426392 895098 702825 664334 681639 576125 451949 945962 249837 142450 266959 175142 680433 > 4949 [i]